Solve for $x$ and $y$ using elimination. ${x-3y = -21}$ ${-x-4y = -42}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-7y = -63$ $\dfrac{-7y}{{-7}} = \dfrac{-63}{{-7}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {x-3y = -21}\thinspace$ to find $x$ ${x - 3}{(9)}{= -21}$ $x-27 = -21$ $x-27{+27} = -21{+27}$ ${x = 6}$ You can also plug ${y = 9}$ into $\thinspace {-x-4y = -42}\thinspace$ and get the same answer for $x$ : ${-x - 4}{(9)}{= -42}$ ${x = 6}$